no unique solution, since you have 4 variables but only 3 equations.
To find some solutions, you could do this:
divide the 3rd by the 2nd
rt/(st) = 21/(2y)
r = 21s/(2y)
sub into the 1st
s(21s)/(2y) = 3y+1
21s^2 = 2y(3y+1)
s^2 = 2y(3y+1)/21
s =√[2y(3y+1)/21 ]
also t = 2y/s and r = 21/t
so you could assign any value to y and get the others
e.g. let y = 1
then s = √(8/21) = appr 6.172
then t = 3.24 and r = 6.48
so (r,s,t,y) = (6.48, .6172, 3.24, 1)
let y = 4
s = √(104/21) = appr 2.225
then t = 3.595 and r = 5.842
(r,s,t,y) = (5.842, 2.225, 3.595, 4)
I checked the above, if you store the 4 numbers in 4 separate memory locations on your calculator, the results are correct.
Without a calculator the above would be a nightmare
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